Simplify the following expression: $z = \dfrac{5}{7y} + \dfrac{1}{3y}$
Answer: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7y$ and $3y$ $\lcm(7y, 3y) = 21y$ $ z = \dfrac{3}{3} \cdot \dfrac{5}{7y} + \dfrac{7}{7} \cdot \dfrac{1}{3y} $ $z = \dfrac{15}{21y} + \dfrac{7}{21y}$ $z = \dfrac{15 +7}{21y}$ $z = \dfrac{22}{21y}$